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inductance is the property of a conductor by which a change in current in the conductor "induces" (creates) a voltage (electromotive force) in both the conductor itself (self-inductance). --wikipedia

From what I understand, the inducing happens due to the resulting change in magnetic field from the change in current

Also, from what I understand, the greater the current, the greater the magnetic field.

However, the inductance of a coil is not dependent on the current. My reasoning behind that is that for every unit of current in the coil, there is a unit of magnetic field which induces an opposing voltage (and in turn current) which is proportional. So if current increases, a proportional amount of opposing current will be there, therefore it cancels out in the formula just like this guy explains:

watch?v=Ab0dJLdmApg

Let me know if I understand everything so far because now my real question comes:

Self induction of a coil is constant. But what if you have a changing magnetic field coming from an external source. Is it possible that the external flux of the magnetic field superimposes with the flux coming from the coil itself to give a net flux of zero? This would mean inductance would be zero and the coil would behave like a straight wire with little or no inductance.

In school I was taught that inductance of a given coil cannot change which is why this question is really bugging me.

Thanks